What is the equation of the give quadratic function?

Question

Y-intercept is (0,24)

X intercepts are (-3,0) and (8,0)

A) f(x)= -x^2+8x+24

B) f(x)=-(-x-3)(x+8)

C) f(x)= x^2-8x+24

D) f(x)= -(x+3)(x-8)

Answer 1

Plug and chug! Since every point on a curve has coordinates that satisfy its equation, all you need to do is carefully plug these three points into the right equation. If you pick the right equation, each and every one of the three points will make it true, e.g. 24 = 24 or 0 = 0 depending which point you use.

Answer 2

Hey Hailey, Hopefully my answer can help you out!

So first we need to define what an x- and y- intercept are. The easiest way to describe them is an x- intercept is when you set y = 0 or in this case 0 = equation, and the y- intercept is when you plug in 0 for x.

So if it's a quadratic, we know that if we plug in 0 and get a number other than 0, than whatever y is equal to is our constant, in this case, 24. Which sadly doesn't eliminate any of our options, which is why we must more onto the x-intercepts.

So in this case we know if we plug in either -3 or 8, we must get 0. So we can plug those into all of our functions to double check. This automatically rules out B, because when you plug in 8 it doesn't become 0. The same goes for C and A, which leaves us with D as the correct answer.

Hopefully this helped!